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Theorem relfth 16772
Description: The set of faithful functors is a relation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Assertion
Ref Expression
relfth Rel (𝐶 Faith 𝐷)

Proof of Theorem relfth
StepHypRef Expression
1 fthfunc 16770 . 2 (𝐶 Faith 𝐷) ⊆ (𝐶 Func 𝐷)
2 relfunc 16725 . 2 Rel (𝐶 Func 𝐷)
3 relss 5344 . 2 ((𝐶 Faith 𝐷) ⊆ (𝐶 Func 𝐷) → (Rel (𝐶 Func 𝐷) → Rel (𝐶 Faith 𝐷)))
41, 2, 3mp2 9 1 Rel (𝐶 Faith 𝐷)
Colors of variables: wff setvar class
Syntax hints:  wss 3723  Rel wrel 5254  (class class class)co 6792   Func cfunc 16717   Faith cfth 16766
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pow 4974  ax-pr 5034  ax-un 7096
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-mo 2623  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3353  df-sbc 3588  df-csb 3683  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-uni 4575  df-iun 4656  df-br 4787  df-opab 4847  df-mpt 4864  df-id 5157  df-xp 5255  df-rel 5256  df-cnv 5257  df-co 5258  df-dm 5259  df-rn 5260  df-res 5261  df-ima 5262  df-iota 5992  df-fun 6031  df-fv 6037  df-ov 6795  df-oprab 6796  df-mpt2 6797  df-1st 7315  df-2nd 7316  df-func 16721  df-fth 16768
This theorem is referenced by:  fthpropd  16784  fthres2  16795  cofth  16798
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